This estimate is not standard because of the behavior of the coefficients of \({\mathcal {L}}\)  at the front faces of \(Q_h\) .
To handle this, we consider the lift of this operator to the blowup. We follow in broud outline a proof of a priori
estimates given by Krylov [1]}, adapted to the present situation. By standard localization and approximation
arguments, it is enough to prove a priori estimates for each of the following simpler model operators near the different
faces of each \(Q_h\) . In the following, we use either the original coordinates \((t,x)\) 
or else the projective coordinates \((\tau ,s)\) .
